Number symbolism in music : the harmony of the spheres and George Crumb's Makrokosmos, Volume I - Pienaar, Elizabeth Angele (College of Music, 2023)
The Pythagoreans, for whom certain numbers held a mystical significance, stressed the connection between music and mathematics. Their concept of the universe was of an integrated, well-ordered system, which expressed the rules of music and mathematics on earthly and planetary levels. This philosophy was adapted by the early Christian church, and numbers that symbolise elements of the Christian faith can be found in medieval compositions. Bach's use of symbolism in sacred works is a continuation of this tradition, but there are numbers of personal significance as well. The numbers ten and twenty-three in Berg's music refer specifically to Hanna Fuchs and himself and have an important structural function. Crumb's compositions are characterised by allusions, especially to music of the past; the symbolic qualities are visual, aural and numerical. Makrokosmos, Volume I (Twelve Fantasy-Pieces after the 'Zodiac for Amplified Piano) is the first in a cycle of four compositions inspired by the stars. Astrological and spiritual numbers-three, four, twelve, seven and five appear to have determined the structural parameters of the pieces.